A. Genz, Zongli Lin, Charles Jones, Dali Luo, Thorsten Prenzel
Numerical results show that a straightforward implementation in MATLAB of an algorithm for the Fast Givens QR Factorization of an m x n matrix takes more time than an implementation of an algorithm that uses ordinary Givens transformations. Results of timing experiments for various operations in MATLAB are reported and models are constructed to explain why the standard theoretical analysis based on flop counts does not account for the actual times for the algorithms.
{"title":"Fast Givens goes slow in MATLAB","authors":"A. Genz, Zongli Lin, Charles Jones, Dali Luo, Thorsten Prenzel","doi":"10.1145/122286.122288","DOIUrl":"https://doi.org/10.1145/122286.122288","url":null,"abstract":"Numerical results show that a straightforward implementation in MATLAB of an algorithm for the Fast Givens QR Factorization of an m x n matrix takes more time than an implementation of an algorithm that uses ordinary Givens transformations. Results of timing experiments for various operations in MATLAB are reported and models are constructed to explain why the standard theoretical analysis based on flop counts does not account for the actual times for the algorithms.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123353462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Householder QR transformation using rank-1 updates and the transformation using rank-2 updates are both O(N3) with the same cubic coefficient. While the rank-1 implementation has the smaller quadratic coefficient, the rank-2 implementation in practice is the faster algorithm, the amount of speed-up varying with the computer. This speed-up is not purely the result of replacing SAXPY operations with double GAXPY ones.
{"title":"Timing comparisons of the householder QR transformations with rank-1 and rank-2 updates","authors":"T. Rolfe","doi":"10.1145/122272.122275","DOIUrl":"https://doi.org/10.1145/122272.122275","url":null,"abstract":"The Householder QR transformation using rank-1 updates and the transformation using rank-2 updates are both O(N3) with the same cubic coefficient. While the rank-1 implementation has the smaller quadratic coefficient, the rank-2 implementation in practice is the faster algorithm, the amount of speed-up varying with the computer. This speed-up is not purely the result of replacing SAXPY operations with double GAXPY ones.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130686028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Ettore Majorana Centre for Scientific Culture (Center) was founded in 1963 to "give life to a completely new way of realizing the EAST-WEST-NORTH-SOUTH collaboration, without discrimination and above any ideological, political, or racial barrier." The Italian Ministry of Education, the Italian Ministry of University and Scientific Research, and the Sicilian Regional Government sponsor the center, located in Erice, Sicily. The center is named for an Italian theoretical unclear physicist, of whom Enrico Fermi said "... and then there are the geniuses like Galileo and Newton. Ettore Majorana was one of these."
{"title":"Topics in computer-aided geometric design-1990","authors":"R. Franke","doi":"10.1145/122272.122274","DOIUrl":"https://doi.org/10.1145/122272.122274","url":null,"abstract":"The Ettore Majorana Centre for Scientific Culture (Center) was founded in 1963 to \"give life to a completely new way of realizing the EAST-WEST-NORTH-SOUTH collaboration, without discrimination and above any ideological, political, or racial barrier.\" The Italian Ministry of Education, the Italian Ministry of University and Scientific Research, and the Sicilian Regional Government sponsor the center, located in Erice, Sicily. The center is named for an Italian theoretical unclear physicist, of whom Enrico Fermi said \"... and then there are the geniuses like Galileo and Newton. Ettore Majorana was one of these.\"","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132357067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper casts doubt on the feasibility of perfect subroutines or perfect hardware for mathematical functions, in particular by conversion from double precision. It suggests a slightly relaxed standard.
{"title":"Feasibility of “perfect” function evaluation","authors":"C. Dunham","doi":"10.1145/122272.122276","DOIUrl":"https://doi.org/10.1145/122272.122276","url":null,"abstract":"This paper casts doubt on the feasibility of perfect subroutines or perfect hardware for mathematical functions, in particular by conversion from double precision. It suggests a slightly relaxed standard.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114108958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The major potential difficulties in obtaining parameters of a model from scientific observations are discussed in the context of the theory of best approximation.
在最佳逼近理论的背景下，讨论了从科学观测中获得模型参数的主要潜在困难。
{"title":"Difficulties in fitting scientific data","authors":"C. Dunham","doi":"10.1145/101064.101068","DOIUrl":"https://doi.org/10.1145/101064.101068","url":null,"abstract":"The major potential difficulties in obtaining parameters of a model from scientific observations are discussed in the context of the theory of best approximation.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114222503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two perennial obstacles to the effective use of software, and especially mathematical software, are its documentation and its user-accessibility. This article surveys some of the ways in which software providers address the issues of documentation and use of their products, and suggests an alternative mechanism for both documentation and access via a hypertext database and command processor. Some considerations relating to program size and complexity and to the security of computer applications are discussed.
{"title":"A hypertext environment for using mathematical software: part 1—motivations and design objectives","authors":"J. Nash","doi":"10.1145/101064.101066","DOIUrl":"https://doi.org/10.1145/101064.101066","url":null,"abstract":"Two perennial obstacles to the effective use of software, and especially mathematical software, are its documentation and its user-accessibility. This article surveys some of the ways in which software providers address the issues of documentation and use of their products, and suggests an alternative mechanism for both documentation and access via a hypertext database and command processor. Some considerations relating to program size and complexity and to the security of computer applications are discussed.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"406 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116513996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When doing simulations one of the worst problems that can occur is an unstable system model. These unstable models often appear in systems identification problems where the system has a non-minimum phase model. This situation leads to an unstable inverse system. The instability means that the system model must be redefined, even though the non-minimum phase model is most accurate. Or a method for deconvolution will be chosen that assumes the system is minimum phase, even though it is not. Often these inaccurate fixes or assumptions are not necessary. Cases where short strings of data are being processed can use the unstable inverse and produce good results. By using the superposition feature of linear systems it is possible to increase the useful run time of these unstable deconvolvers.
{"title":"Slowing propagation error caused by finite register sizes in unstable systems","authors":"S. Cynar","doi":"10.1145/101064.101069","DOIUrl":"https://doi.org/10.1145/101064.101069","url":null,"abstract":"When doing simulations one of the worst problems that can occur is an unstable system model. These unstable models often appear in systems identification problems where the system has a non-minimum phase model. This situation leads to an unstable inverse system. The instability means that the system model must be redefined, even though the non-minimum phase model is most accurate. Or a method for deconvolution will be chosen that assumes the system is minimum phase, even though it is not. Often these inaccurate fixes or assumptions are not necessary. Cases where short strings of data are being processed can use the unstable inverse and produce good results. By using the superposition feature of linear systems it is possible to increase the useful run time of these unstable deconvolvers.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132098914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. H. Wilkinson, in justifying backward error analyses, advanced the proposition that a numerical routine could not be blamed if the computed answer was the exact answer to the problem with slightly perturbed input. Such a model was established by Wilkinson (1968) for the solution of linear equations, ns by (I) Gaussian elimination and (II) triangular decomposition using double precision accumulation of inner products. In the latter it is usual that inputs are perturbed only by a small multiple of a unit rounding error (see formula (175)).
j·h·威尔金森(J. H. Wilkinson)在证明反向误差分析的合理性时，提出了这样一个命题:如果计算出的答案是输入稍有扰动的问题的确切答案，那么数值程序就不会受到指责。这种模型是由Wilkinson(1968)建立的，用于求解线性方程，通过(I)高斯消去和(II)使用双精度累积内积的三角分解。在后一种情况下，输入通常只受到单位舍入误差的一个小倍数的干扰(见公式(175))。
{"title":"How accurate should numerical routines be?","authors":"C. Dunham","doi":"10.1145/101070.101074","DOIUrl":"https://doi.org/10.1145/101070.101074","url":null,"abstract":"J. H. Wilkinson, in justifying backward error analyses, advanced the proposition that a numerical routine could not be blamed if the computed answer was the exact answer to the problem with slightly perturbed input. Such a model was established by Wilkinson (1968) for the solution of linear equations, ns by (I) Gaussian elimination and (II) triangular decomposition using double precision accumulation of inner products. In the latter it is usual that inputs are perturbed only by a small multiple of a unit rounding error (see formula (175)).","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132769079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonlinear least squares problem is a special case of the unconstrained minimization problem. While a large number of new algorithms have been developed in recent years, both for general unconstrained minimization and the least squares case, comparative studies are limited. Further, there has been practically a revolution in algorithm testing and comparison methodology. Recent advances include a more comprehensive performance criteria, use of large numbers of randomly generated test problems, and application of sophisticated statistical techniques for experiment design and data evaluation.These developments have made questionable the findings of the few earlier comparative studies of least squares algorithms. This creates a necessity of a comparative study employing current methodology that evaluates the specialized least squares algorithms along with a few general algorithms for unconstrained minimization.
{"title":"A note on comparison of nonlinear least squares algorithms","authors":"Zafar Khan, Sudhir Chawla, Dinesh Dave","doi":"10.1145/101070.101075","DOIUrl":"https://doi.org/10.1145/101070.101075","url":null,"abstract":"The nonlinear least squares problem is a special case of the unconstrained minimization problem. While a large number of new algorithms have been developed in recent years, both for general unconstrained minimization and the least squares case, comparative studies are limited. Further, there has been practically a revolution in algorithm testing and comparison methodology. Recent advances include a more comprehensive performance criteria, use of large numbers of randomly generated test problems, and application of sophisticated statistical techniques for experiment design and data evaluation.These developments have made questionable the findings of the few earlier comparative studies of least squares algorithms. This creates a necessity of a comparative study employing current methodology that evaluates the specialized least squares algorithms along with a few general algorithms for unconstrained minimization.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115779096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A computational algorithm for an efficient LU decomposition of a sequence of matrices that differ in one or more elements is presented and some possible areas of engineering and business applications are outlined. CPU time, as measured in an implementation of the algorithm using FORTRAN code, is shown to agree very well with the estimated operations count.
{"title":"A computational algorithm for LU decomposition of a sequence of matrices that differ only in one or more elements","authors":"M. Zahir","doi":"10.1145/74654.74656","DOIUrl":"https://doi.org/10.1145/74654.74656","url":null,"abstract":"A computational algorithm for an efficient LU decomposition of a sequence of matrices that differ in one or more elements is presented and some possible areas of engineering and business applications are outlined. CPU time, as measured in an implementation of the algorithm using FORTRAN code, is shown to agree very well with the estimated operations count.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117198015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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